0.03/0.33 WORST_CASE(?,O(n^1)) 0.03/0.33 0.03/0.33 Preprocessing Cost Relations 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 #### Computed strongly connected components 0.03/0.33 0. recursive : [eval_start_bb1_in/7,eval_start_bb2_in/7,eval_start_bb3_in/7,eval_start_bb4_in/7] 0.03/0.33 1. non_recursive : [eval_start_stop/5] 0.03/0.33 2. non_recursive : [eval_start_bb5_in/5] 0.03/0.33 3. non_recursive : [exit_location/1] 0.03/0.33 4. non_recursive : [eval_start_bb1_in_loop_cont/6] 0.03/0.33 5. non_recursive : [eval_start_8/5] 0.03/0.33 6. non_recursive : [eval_start_7/5] 0.03/0.33 7. non_recursive : [eval_start_6/5] 0.03/0.33 8. non_recursive : [eval_start_5/5] 0.03/0.33 9. non_recursive : [eval_start_4/5] 0.03/0.33 10. non_recursive : [eval_start_3/5] 0.03/0.33 11. non_recursive : [eval_start_2/5] 0.03/0.33 12. non_recursive : [eval_start_1/5] 0.03/0.33 13. non_recursive : [eval_start_0/5] 0.03/0.33 14. non_recursive : [eval_start_bb0_in/5] 0.03/0.33 15. non_recursive : [eval_start_start/5] 0.03/0.33 0.03/0.33 #### Obtained direct recursion through partial evaluation 0.03/0.33 0. SCC is partially evaluated into eval_start_bb1_in/7 0.03/0.33 1. SCC is completely evaluated into other SCCs 0.03/0.33 2. SCC is completely evaluated into other SCCs 0.03/0.33 3. SCC is completely evaluated into other SCCs 0.03/0.33 4. SCC is partially evaluated into eval_start_bb1_in_loop_cont/6 0.03/0.33 5. SCC is partially evaluated into eval_start_8/5 0.03/0.33 6. SCC is completely evaluated into other SCCs 0.03/0.33 7. SCC is completely evaluated into other SCCs 0.03/0.33 8. SCC is completely evaluated into other SCCs 0.03/0.33 9. SCC is completely evaluated into other SCCs 0.03/0.33 10. SCC is completely evaluated into other SCCs 0.03/0.33 11. SCC is completely evaluated into other SCCs 0.03/0.33 12. SCC is completely evaluated into other SCCs 0.03/0.33 13. SCC is completely evaluated into other SCCs 0.03/0.33 14. SCC is completely evaluated into other SCCs 0.03/0.33 15. SCC is partially evaluated into eval_start_start/5 0.03/0.33 0.03/0.33 Control-Flow Refinement of Cost Relations 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_start_bb1_in/7 0.03/0.33 * CE 3 is refined into CE [9] 0.03/0.33 * CE 6 is refined into CE [10] 0.03/0.33 * CE 5 is refined into CE [11] 0.03/0.33 * CE 4 is refined into CE [12] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_start_bb1_in/7 0.03/0.33 * CEs [11] --> Loop 9 0.03/0.33 * CEs [12] --> Loop 10 0.03/0.33 * CEs [9] --> Loop 11 0.03/0.33 * CEs [10] --> Loop 12 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_start_bb1_in(V_m,V_n,V_x_0,V_y_0,B,C,D) 0.03/0.33 * RF of phase [9]: [V_n-V_x_0,V_n-V_y_0] 0.03/0.33 * RF of phase [10]: [V_m-V_x_0,V_m-V_y_0] 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_start_bb1_in(V_m,V_n,V_x_0,V_y_0,B,C,D) 0.03/0.33 * Partial RF of phase [9]: 0.03/0.33 - RF of loop [9:1]: 0.03/0.33 V_n-V_x_0 0.03/0.33 V_n-V_y_0 0.03/0.33 * Partial RF of phase [10]: 0.03/0.33 - RF of loop [10:1]: 0.03/0.33 V_m-V_x_0 0.03/0.33 V_m-V_y_0 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_start_bb1_in_loop_cont/6 0.03/0.33 * CE 8 is refined into CE [13] 0.03/0.33 * CE 7 is refined into CE [14] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/6 0.03/0.33 * CEs [13] --> Loop 13 0.03/0.33 * CEs [14] --> Loop 14 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_start_8/5 0.03/0.33 * CE 2 is refined into CE [15,16,17,18,19,20,21,22] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_start_8/5 0.03/0.33 * CEs [16,20] --> Loop 15 0.03/0.33 * CEs [22] --> Loop 16 0.03/0.33 * CEs [18] --> Loop 17 0.03/0.33 * CEs [17,21] --> Loop 18 0.03/0.33 * CEs [19] --> Loop 19 0.03/0.33 * CEs [15] --> Loop 20 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_start_8(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_start_8(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_start_start/5 0.03/0.33 * CE 1 is refined into CE [23,24,25,26,27,28] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_start_start/5 0.03/0.33 * CEs [28] --> Loop 21 0.03/0.33 * CEs [27] --> Loop 22 0.03/0.33 * CEs [26] --> Loop 23 0.03/0.33 * CEs [25] --> Loop 24 0.03/0.33 * CEs [24] --> Loop 25 0.03/0.33 * CEs [23] --> Loop 26 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_start_start(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_start_start(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.33 0.03/0.33 0.03/0.33 Computing Bounds 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 #### Cost of chains of eval_start_bb1_in(V_m,V_n,V_x_0,V_y_0,B,C,D): 0.03/0.33 * Chain [[10],12]: 1*it(10)+0 0.03/0.33 Such that:it(10) =< V_m-V_x_0 0.03/0.33 0.03/0.33 with precondition: [B=2,V_x_0=V_y_0,V_x_0>=0,V_x_0>=V_n,V_m>=V_x_0+1] 0.03/0.33 0.03/0.33 * Chain [[10],11]: 1*it(10)+0 0.03/0.33 Such that:it(10) =< -V_x_0+D 0.03/0.33 0.03/0.33 with precondition: [B=3,V_x_0=V_y_0,V_m=C,V_m=D,V_x_0>=0,V_x_0>=V_n,V_m>=V_x_0+1] 0.03/0.33 0.03/0.33 * Chain [[9],[10],12]: 1*it(9)+1*it(10)+0 0.03/0.33 Such that:it(10) =< V_m-V_n 0.03/0.33 it(9) =< V_n-V_y_0 0.03/0.33 0.03/0.33 with precondition: [B=2,V_x_0=V_y_0,V_x_0>=0,V_m>=V_n+1,V_n>=V_x_0+1] 0.03/0.33 0.03/0.33 * Chain [[9],[10],11]: 1*it(9)+1*it(10)+0 0.03/0.33 Such that:it(10) =< -V_n+D 0.03/0.33 it(9) =< V_n-V_y_0 0.03/0.33 0.03/0.33 with precondition: [B=3,V_x_0=V_y_0,V_m=C,V_m=D,V_x_0>=0,V_m>=V_n+1,V_n>=V_x_0+1] 0.03/0.33 0.03/0.33 * Chain [[9],12]: 1*it(9)+0 0.03/0.33 Such that:it(9) =< V_n-V_y_0 0.03/0.33 0.03/0.33 with precondition: [B=2,V_x_0=V_y_0,V_x_0>=0,V_n>=V_x_0+1] 0.03/0.33 0.03/0.33 * Chain [[9],11]: 1*it(9)+0 0.03/0.33 Such that:it(9) =< -V_x_0+D 0.03/0.33 0.03/0.33 with precondition: [B=3,V_x_0=V_y_0,V_n=C,V_n=D,V_x_0>=0,V_n>=V_m,V_n>=V_x_0+1] 0.03/0.33 0.03/0.33 * Chain [12]: 0 0.03/0.33 with precondition: [B=2,V_y_0=V_x_0,V_y_0>=0] 0.03/0.33 0.03/0.33 * Chain [11]: 0 0.03/0.33 with precondition: [B=3,V_y_0=V_x_0,V_y_0=C,V_y_0=D,V_y_0>=0,V_y_0>=V_m,V_y_0>=V_n] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.33 * Chain [14]: 0 0.03/0.33 with precondition: [A=2] 0.03/0.33 0.03/0.33 * Chain [13]: 0 0.03/0.33 with precondition: [A=3] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of eval_start_8(V_m,V_n,V_x_0,V_y_0,B): 0.03/0.33 * Chain [20]: 0 0.03/0.33 with precondition: [] 0.03/0.33 0.03/0.33 * Chain [19]: 0 0.03/0.33 with precondition: [0>=V_m,0>=V_n] 0.03/0.33 0.03/0.33 * Chain [18]: 2*s(1)+0 0.03/0.33 Such that:aux(1) =< V_m 0.03/0.33 s(1) =< aux(1) 0.03/0.33 0.03/0.33 with precondition: [0>=V_n,V_m>=1] 0.03/0.33 0.03/0.33 * Chain [17]: 1*s(3)+0 0.03/0.33 Such that:s(3) =< V_n 0.03/0.33 0.03/0.33 with precondition: [V_n>=1] 0.03/0.33 0.03/0.33 * Chain [16]: 1*s(4)+0 0.03/0.33 Such that:s(4) =< V_n 0.03/0.33 0.03/0.33 with precondition: [V_n>=1,V_n>=V_m] 0.03/0.33 0.03/0.33 * Chain [15]: 2*s(5)+2*s(6)+0 0.03/0.33 Such that:aux(2) =< V_m-V_n 0.03/0.33 aux(3) =< V_n 0.03/0.33 s(5) =< aux(2) 0.03/0.33 s(6) =< aux(3) 0.03/0.33 0.03/0.33 with precondition: [V_n>=1,V_m>=V_n+1] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of eval_start_start(V_m,V_n,V_x_0,V_y_0,B): 0.03/0.33 * Chain [26]: 0 0.03/0.33 with precondition: [] 0.03/0.33 0.03/0.33 * Chain [25]: 0 0.03/0.33 with precondition: [0>=V_m,0>=V_n] 0.03/0.33 0.03/0.33 * Chain [24]: 2*s(10)+0 0.03/0.33 Such that:s(9) =< V_m 0.03/0.33 s(10) =< s(9) 0.03/0.33 0.03/0.33 with precondition: [0>=V_n,V_m>=1] 0.03/0.33 0.03/0.33 * Chain [23]: 1*s(11)+0 0.03/0.33 Such that:s(11) =< V_n 0.03/0.33 0.03/0.33 with precondition: [V_n>=1] 0.03/0.33 0.03/0.33 * Chain [22]: 1*s(12)+0 0.03/0.33 Such that:s(12) =< V_n 0.03/0.33 0.03/0.33 with precondition: [V_n>=1,V_n>=V_m] 0.03/0.33 0.03/0.33 * Chain [21]: 2*s(15)+2*s(16)+0 0.03/0.33 Such that:s(13) =< V_m-V_n 0.03/0.33 s(14) =< V_n 0.03/0.33 s(15) =< s(13) 0.03/0.33 s(16) =< s(14) 0.03/0.33 0.03/0.33 with precondition: [V_n>=1,V_m>=V_n+1] 0.03/0.33 0.03/0.33 0.03/0.33 Closed-form bounds of eval_start_start(V_m,V_n,V_x_0,V_y_0,B): 0.03/0.33 ------------------------------------- 0.03/0.33 * Chain [26] with precondition: [] 0.03/0.33 - Upper bound: 0 0.03/0.33 - Complexity: constant 0.03/0.33 * Chain [25] with precondition: [0>=V_m,0>=V_n] 0.03/0.33 - Upper bound: 0 0.03/0.33 - Complexity: constant 0.03/0.33 * Chain [24] with precondition: [0>=V_n,V_m>=1] 0.03/0.33 - Upper bound: 2*V_m 0.03/0.33 - Complexity: n 0.03/0.33 * Chain [23] with precondition: [V_n>=1] 0.03/0.33 - Upper bound: V_n 0.03/0.33 - Complexity: n 0.03/0.33 * Chain [22] with precondition: [V_n>=1,V_n>=V_m] 0.03/0.33 - Upper bound: V_n 0.03/0.33 - Complexity: n 0.03/0.33 * Chain [21] with precondition: [V_n>=1,V_m>=V_n+1] 0.03/0.33 - Upper bound: 2*V_m 0.03/0.33 - Complexity: n 0.03/0.33 0.03/0.33 ### Maximum cost of eval_start_start(V_m,V_n,V_x_0,V_y_0,B): max([nat(V_m)*2,nat(V_m-V_n)*2+nat(V_n)+nat(V_n)]) 0.03/0.33 Asymptotic class: n 0.03/0.33 * Total analysis performed in 259 ms. 0.03/0.33 0.03/0.43 EOF